1. Field of the Invention
The present invention generally relates to spread-spectrum (SS) systems. In particular, the present invention relates to systems, methods and apparatus for correlating a received SS signal with all lags of a reference code sequence and producing all correlation lags at a sampling instant.
2. Description of the Related Art
SS techniques have applications in many areas such as secure communications, multiple-access communications, channel sounding, ranging and target identification using radars and sonars, and navigation using Global Positioning System (GPS) or GLONASS. One of the essential elements in the implementation of a SS receiver is a correlator. A correlator is required at the receiver to initially acquire or code-align the incoming SS signal with the pseudo-noise (PN) sequence that is identical to the one used at the transmitter side to spread the signal. A correlator is also used to perform other functions such as code tracking, symbol and carrier recovery, demodulation of information symbols embedded in the SS signal, and channel estimation. A correlator correlates a sequence of N samples in a stream of incoming SS signal samples {dn} with a code sequence {c0, c1, . . . , cN−1}, where N is the length of the code sequence, and generates a correlation resultun=c0dn−(N−1)+c1dn−(N−2)+c2dn−(n−3) . . . +cN−2dn−1+cN−1dn  (1) at the nth sampling instant. Herein the code sequence is referred to as a reference code. The reference-code length N is normally selected such that it is equal to the length of the PN sequence that is used to spread the SS signal, L, multiplied by the number of samples per chip, K, where K is a positive integer.
A serial correlator generates correlation values at a rate equal to one per N signal samples. That is, a serial correlator generates . . . , u−2N, u−N, u0, uN, u2N, . . . . It is possible that the incoming signal samples are not code-aligned with the reference code. There is then a (time) lag between the incoming signal samples and the reference code. A serial correlator can only generate a correlation value at a particular lag. This correlation value is herein referred to as a correlation lag. Computation of a different correlation lag requires shifting or delaying/advancing the incoming signal. A parallel correlator, on the other hand, generates correlation lags at a rate equal to the rate of the incoming signal samples. Since the reference-code length is N, it is required to compute N correlation values corresponding to correlating the signal with 0, 1, . . . , N−1 lags of the reference code. A parallel correlator is therefore required to compute N correlation lags, given by                                                                         u                n                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      1                                                                      +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                  n                                                                                                                        u                                  n                  +                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                    n                                                  +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    +                    1                                                                                                                                          u                                  n                  +                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          5                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      +                      1                                                                      +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    +                    2                                                                                                                          ⋮              ⁢                                                                                                                                       u                                  n                  +                  N                  -                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                      1                                                                      +                                                      c                    1                                    ⁢                                      d                    n                                                  +                                                      c                    2                                    ⁢                                      d                                          n                      +                      1                                                                      +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      +                      N                      -                      3                                                                      +                                                      c                                          N                      -                      1                                                        ⁢                                      d                                          n                      +                      N                      -                      2                                                                                                                                                                                u                                      n                    +                    N                    -                    1                                                  =                                ⁢                                                                            c                      0                                        ⁢                                          d                      n                                                        +                                                            c                      1                                        ⁢                                          d                                              n                        +                        1                                                                              +                                                            c                      2                                        ⁢                                          d                                              n                        +                        2                                                                              +                  ⋯                  +                                                            c                                              N                        -                        2                                                              ⁢                                          d                                              n                        +                        N                        -                        2                                                                              +                                                            c                                              N                        -                        1                                                              ⁢                                          d                                              n                        +                        N                        -                        1                                                                                                        ,                                                          (        2        )            over a duration of N consecutive sampling intervals.
If the SS signal under consideration is a signal generated by means of periodic repetition of a PN sequence without data modulation, then the intended information obtained in the sample dn+1 is also contained in dn−(N−1). Similarly, the information contained in dn+2, dn+3, . . . , dn+N−1 is also contained in dn−(N−2), dn−(N−3), . . . , dn−1. Thus, equation (2) can be equivalently expressed as                                                                         u                n                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      1                                                                      +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                  n                                                                                                                        u                                  n                  +                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                    n                                                  +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        1                                            )                                                                                                                                                              u                                  n                  +                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          5                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        2                                            )                                                                                                                                              ⋮              ⁢                                                                                                                                       u                                  n                  +                  N                  -                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                      1                                                                      +                                                      c                    1                                    ⁢                                      d                    n                                                  +                                                      c                    2                                    ⁢                                      d                                          n                      +                                              (                                                  N                          -                          1                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      3                                                                      +                                                      c                                          N                      -                      1                                                        ⁢                                      d                                          n                      -                      2                                                                                                                                                              u                                  n                  +                  N                  -                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                    n                                                  +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      2                                                                      +                                                      c                                          N                      -                      1                                                        ⁢                                                            d                                              n                        -                        1                                                              .                                                                                                          (        3        )            Thus, computation of un, un+1, . . . , un+N−1 is equivalent to computing rn=[r0,n, r1,n, . . . , rN−1,n]T from a block of data samples dn, dn−1, . . . , dn−(N−1), where                               [                                                                      r                                      0                    ,                    n                                                                                                                        r                                      1                    ,                    n                                                                                                                        r                                      2                    ,                    n                                                                                                      ⋮                                                                                      r                                                            N                      -                      2                                        ,                    n                                                                                                                        r                                                            N                      -                      1                                        ,                    n                                                                                ]                =                                            [                                                                                          c                      0                                                                                                  c                      1                                                                                                  c                      2                                                                            ⋯                                                                              c                                              N                        -                        2                                                                                                                        c                                              N                        -                        1                                                                                                                                                        c                                              N                        -                        1                                                                                                                        c                      0                                                                                                  c                      1                                                                            ⋯                                                                              c                                              N                        -                        3                                                                                                                        c                                              N                        -                        2                                                                                                                                                        c                                              N                        -                        2                                                                                                                        c                                              N                        -                        1                                                                                                                        c                      0                                                                            ⋯                                                                              c                                              N                        -                        4                                                                                                                        c                                              N                        -                        4                                                                                                                                  ⋮                                                        ⋮                                                        ⋮                                                        ⋰                                                        ⋮                                                        ⋮                                                                                                              c                      2                                                                                                  c                      3                                                                                                  c                      4                                                                            ⋯                                                                              c                      0                                                                                                  c                      1                                                                                                                                  c                      1                                                                                                  c                      2                                                                                                  c                      3                                                                            ⋯                                                                              c                                              N                        -                        1                                                                                                                        c                      0                                                                                  ]                        ⁡                          [                                                                                          d                                              n                        -                                                  (                                                      N                            -                            1                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            2                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            3                                                    )                                                                                                                                                          ⋮                                                                                                              d                                                                        n                          -                          1                                                )                                                                                                                                                        d                      n                                                                                  ]                                .                                    (        4        )            Thus, rn is a set of correlations for all lags or simply a set of all correlation lags.
The sequence of sets of all correlation lags, {rn}, is generated at a rate equal to the rate of incoming SS signal samples {dn}. It is obvious that a means for generating an all-lag correlation sequence can be implemented by means of N parallel correlators each of which correlates SS signal samples with the reference code at a given lag. However, none of the prior art teaches or suggests a method or apparatus for correlating a received SS signal with a reference code using a single correlator (a) which has the number of outputs equal to the length of the reference code and (b) whose outputs at one sampling instant are all correlation lags for the incoming SS signal samples and are produced at a rate equal to the rate of the incoming SS signal samples.
For example, the SS signal under consideration could be a signal composed by means of modulating data with the entirety of a PN sequence. When successive data symbols contained in signal samples dn−(N−1), dn−(N−2), . . . , dn+N−1 have the same sign, the intended information obtained in the sample dn+1 is also contained in dn−(N−1). Similarly, the information contained in dn+2, dn+3, . . . , dn+N−1 is also contained in dn−(N−2), dn−(N−3), . . . , dn−1. Thus, equation (2) can be equivalently expressed as                                                                         u                n                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      1                                                                      +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                  n                                                                                                                        u                                  n                  +                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                    n                                                  +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        1                                            )                                                                                                                                                              u                                  n                  +                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          5                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        2                                            )                                                                                                                                              ⋮              ⁢                                                                                                                                       u                                  n                  +                  N                  -                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                      1                                                                      +                                                      c                    1                                    ⁢                                      d                    n                                                  +                                                      c                    2                                    ⁢                                      d                                          n                      +                                              (                                                  N                          -                          1                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      3                                                                      +                                                      c                                          N                      -                      1                                                        ⁢                                      d                                          n                      -                      2                                                                                                                                                                                u                                      n                    +                    N                    -                    1                                                  =                                ⁢                                                                            c                      0                                        ⁢                                          d                      n                                                        +                                                            c                      1                                        ⁢                                          d                                              n                        -                                                  (                                                      N                            -                            1                                                    )                                                                                                      +                                                            c                      2                                        ⁢                                          d                                              n                        -                                                  (                                                      N                            -                            2                                                    )                                                                                                      +                  ⋯                  +                                                            c                                              N                        -                        2                                                              ⁢                                          d                                              n                        -                        2                                                                              +                                                            c                                              N                        -                        1                                                              ⁢                                          d                                              n                        -                        1                                                                                                        ,                                                          (        5        )            which is the same as equation (3). When successive data symbols contained in signal samples dn−(N−1), dn−(N−2), . . . , dn+N−1 have opposite sign, the intended information obtained in the sample dn+1 is also contained in −dn−(N−1). Similarly, the information contained in dn+2, dn+3, . . . , dn+N−1 is also contained in −dn−(N−2), −dn−(N−3), . . . , −dn−1. Thus, equation (2) becomes                                                                         u                n                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      1                                                                      +                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                  n                                                                                                                        u                                  n                  +                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                ⋯                +                                                      c                                          N                      -                      2                                                        ⁢                                      d                    n                                                  -                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        1                                            )                                                                                                                                                              u                                  n                  +                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          3                                                )                                                                                            +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          4                                                )                                                                                            +                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          5                                                )                                                                                            +                ⋯                -                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            -                                                                                                      ⁢                                                c                                      N                    -                    1                                                  ⁢                                  d                                      n                    -                                          (                                              N                        -                        2                                            )                                                                                                                                              ⋮              ⁢                                                                                                                                       u                                  n                  +                  N                  -                  2                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                                          n                      -                      1                                                                      +                                                      c                    1                                    ⁢                                      d                    n                                                  -                                                      c                    2                                    ⁢                                      d                                          n                      +                                              (                                                  N                          -                          1                                                )                                                                                            +                ⋯                -                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      3                                                                      -                                                      c                                          N                      -                      1                                                        ⁢                                      d                                          n                      -                      2                                                                                                                                                              u                                  n                  +                  N                  -                  1                                            =                            ⁢                                                                    c                    0                                    ⁢                                      d                    n                                                  +                                                      c                    1                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          1                                                )                                                                                            -                                                      c                    2                                    ⁢                                      d                                          n                      -                                              (                                                  N                          -                          2                                                )                                                                                            +                ⋯                -                                                      c                                          N                      -                      2                                                        ⁢                                      d                                          n                      -                      2                                                                      -                                                      c                                          N                      -                      1                                                        ⁢                                                            d                                              n                        -                        1                                                              .                                                                                                          (        6        )            Based on equations (5) and (6), it is clear that computation of un, un+1, . . . , un+(N−1) is equivalent to computing rn=[r0,n,r1,n, . . . ,rN−1,n]T and sn=[s0,n,s1,n, . . . ,sN−1,n]T from a block of data samples dn, dn−1, . . . , dn−(N−1), where                                           [                                                                                r                                          0                      ,                      n                                                                                                                                        r                                          1                      ,                      n                                                                                                                                        r                                          2                      ,                      n                                                                                                                    ⋮                                                                                                  r                                                                  N                        -                        2                                            ,                      n                                                                                                                                        r                                                                  N                        -                        1                                            ,                      n                                                                                            ]                    =                                    [                                                                                          c                      0                                                                                                  c                      1                                                                                                  c                      2                                                                            ⋯                                                                              c                                              N                        -                        2                                                                                                                        c                                              N                        -                        1                                                                                                                                                        c                                              N                        -                        1                                                                                                                        c                      0                                                                                                  c                      1                                                                            ⋯                                                                              c                                              N                        -                        3                                                                                                                        c                                              N                        -                        2                                                                                                                                                        c                                              N                        -                        2                                                                                                                        c                                              N                        -                        1                                                                                                                        c                      0                                                                            ⋯                                                                              c                                              N                        -                        4                                                                                                                        c                                              N                        -                        4                                                                                                                                  ⋮                                                        ⋮                                                        ⋮                                                        ⋰                                                        ⋮                                                        ⋮                                                                                                              c                      2                                                                                                  c                      3                                                                                                  c                      4                                                                            ⋯                                                                              c                      0                                                                                                  c                      1                                                                                                                                  c                      1                                                                                                  c                      2                                                                                                  c                      3                                                                            ⋯                                                                              c                                              N                        -                        1                                                                                                                        c                      0                                                                                  ]                        ⁡                          [                                                                                          d                                              n                        -                                                  (                                                      N                            -                            1                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            2                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            3                                                    )                                                                                                                                                          ⋮                                                                                                              d                                                                        n                          -                          1                                                )                                                                                                                                                        d                      n                                                                                  ]                                      ,        and                            (        7        )                                          [                                                                      s                                      0                    ,                    n                                                                                                                        s                                      1                    ,                    n                                                                                                                        s                                      2                    ,                    n                                                                                                      ⋮                                                                                      s                                                            N                      -                      2                                        ,                    n                                                                                                                        s                                                            N                      -                      1                                        ,                    n                                                                                ]                =                                            [                                                                                          c                      0                                                                                                  c                      1                                                                                                  c                      2                                                                            ⋯                                                                              c                                              N                        -                        2                                                                                                                        c                                              N                        -                        1                                                                                                                                                        -                                              c                                                  N                          -                          1                                                                                                                                                c                      0                                                                                                  c                      1                                                                            ⋯                                                                              c                                              N                        -                        3                                                                                                                        c                                              N                        -                        2                                                                                                                                                        -                                              c                                                  N                          -                          2                                                                                                                                                -                                              c                                                  N                          -                          1                                                                                                                                                c                      0                                                                            ⋯                                                                              c                                              N                        -                        4                                                                                                                        c                                              N                        -                        4                                                                                                                                  ⋮                                                        ⋮                                                        ⋮                                                        ⋰                                                        ⋮                                                        ⋮                                                                                                              -                                              c                        2                                                                                                                        -                                              c                        3                                                                                                                        -                                              c                        4                                                                                                  ⋯                                                                              c                      0                                                                                                  c                      1                                                                                                                                  -                                              c                        1                                                                                                                        -                                              c                        2                                                                                                                        -                                              c                        3                                                                                                  ⋯                                                                              -                                              c                                                  N                          -                          1                                                                                                                                                c                      0                                                                                  ]                        ⁡                          [                                                                                          d                                              n                        -                                                  (                                                      N                            -                            1                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            2                                                    )                                                                                                                                                                                d                                              n                        -                                                  (                                                      N                            -                            3                                                    )                                                                                                                                                          ⋮                                                                                                              d                                                                        n                          -                          1                                                )                                                                                                                                                        d                      n                                                                                  ]                                .                                    (        8        )            Equation (7) is the same as equation (4). The all-lag correlation rn is thus a set of even correlations for all lags and sn is thus a set of odd correlations for all lags.
The sequence of sets of all even-correlation lags, {rn}, and the sequence of sets of all odd-correlation lags, {sn}, are generated at a rate equal to the rate of incoming SS signal samples {dn}. It is obvious that a means for generating an all-lag even-correlation sequence can be implemented by means of N parallel correlators each of which correlates SS signal samples with the reference code at a given lag. It is also obvious that a means for generating an all-lag odd-correlation sequence can be implemented by means of N parallel correlators each of which correlates SS signal samples with a sequence specified by a row of the square matrix in equation (8).
None of the prior art, however, teaches or suggests a method or apparatus for correlating a received SS signal with a reference code using a single correlator (a) which has the number of outputs equal to the length of the reference code and (b) whose outputs at one sampling instant are all even-correlation lags for the incoming SS signal samples and are produced at a rate equal to the rate of the incoming SS signal samples. In addition, none of the prior art teaches or suggests a method or apparatus for correlating a received SS signal with a reference code using a single correlator (a) which has the number of outputs equal to the length of the reference code and (b) whose outputs at one sampling instant are all odd-correlation lags for the incoming SS signal samples and are produced at a rate equal to the rate of the incoming SS signal samples.